A zookeeper is monitoring the population of birds. The flock needs to have exactly three times more females than males to thrive, and the zoo only has room for a maximum of 20 male birds. Let x represent the number of male birds and y represent the number of female birds. Write the constraints to represent a thriving population of birds at the zoo. (1 point)

x > 0 and y > 0

0 < x ≤ 20 and y > 60

x > 0 and y < 20

0 < x ≤ 20 and 0 < y ≤ 60


To solve this, we need to represent the constraints for a thriving population of birds, where:

- \( x \) is the number of male birds,
- \( y \) is the number of female birds.

The problem provides two key conditions:

1. **Thriving condition**: The population must have exactly three times as many females as males, so we know that:
   \[
   y = 3x
   \]
2. **Capacity condition**: The zoo has room for a maximum of 20 male birds, which gives us the inequality:
   \[
   0 < x \leq 20
   \]

### Step-by-step Analysis:
- Since \( y = 3x \), for the population to thrive, \( y \) will always be greater than 60 when \( x \) is at its maximum because \( 3 \times 20 = 60 \).
- For this relationship to hold, \( y > 60 \) when \( x \) is at its minimum (greater than 0). Thus, \( y > 60 \) must be true.

### Therefore, the correct set of constraints is:
\[
0 < x \leq 20 \quad \text{and} \quad y > 60
\]

This matches the option:
**0 < x ≤ 20 and y > 60**

Would you like more details, or do you have any questions? Here are 5 questions you might consider next:
1. How can you model this situation graphically on a coordinate plane?
2. What happens to the population if the number of male birds exceeds 20?
3. How do we account for an uneven number of male and female birds?
4. What if the zoo could house more males? How would the constraints change?
5. Can this problem be expanded to include additional constraints, such as food availability?

**Tip**: Always carefully consider inequalities when modeling real-world constraints in mathematical problems.

A zookeeper is monitoring the population of birds. The flock needs to have exactly three times more females than males to thrive, and the zoo only has room for a maximum of 20 male birds. Let x represent the number of male birds and y represent the number of female birds. Write the constraints to represent a thriving population of birds at the zoo.

Explore the constraints required for a thriving bird population in a zoo setting. Learn how to represent proportional relationships and inequalities where the female bird count must be three times that of males, with a maximum of 20 male birds. Suitable for students in Grades 7-9.

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